Most techniques in relation to a quantum error-correcting code, which are in progress, tend to make a new quantum error-correcting code by applying an existing error-correcting code designing technique.
Quantum error-correcting codes may be generally classified into linear codes and nonlinear codes depending on their configuring manners.
Among nonlinear codes, a stabilizer code proposes a method for easily configuring a quantum error-correcting code which satisfies a dual-containing condition in an existing linear block code, and most quantum error-correcting code techniques are being developed based on the stabilizer code.
Recently, a codeword stabilized quantum (CWS) code capable of describing both linear code and nonlinear code has been proposed as a more generalized code designing technique.
The CWS code may propose a technique capable of designing a quantum error-correcting code by using an existing error-correcting code.
In the quantum error-correcting code, a linear code allows easy configuring and expanding but may be inferior to the maximum performance of a code which may be obtained from a nonlinear code, and a nonlinear code is capable of exhibiting better performance in comparison to a linear code but is not yet being developed diversely since it is not easily configured.
Since it is difficult to configure a nonlinear quantum code, various nonlinear quantum error-correcting codes have not yet been developed, and an error correctable by nonlinear codes which have been developed based on a circular graph until now, including CWS codes, is limited to a single error.
Recently, a technique for designing entanglement-assisted quantum error-correcting codes (EAQECCs) has been proposed. The EAQECCs technique may propose a method for designing a quantum error-correcting code from existing linear block codes without a dual-containing condition of a stabilizer code by applying an entangled qubit (ebit) to the stabilizer code.
Recent study on the EAQECCs shows that the performance of a stabilizer code can be improved by using ebit.